This Appendix describes the methods used in this report to make sea level rise
projections for the SRES scenarios for the 21st century. The results are discussed
in Section 11.5.1.2 and shown in Figure
11.12 and Appendix II.

Global-average sea-level rise h(t)
is a function of time t and is expressed relative to the level in 1990. It comprises
several components, which are all zero at 1990:

The components are sea-level rise due to:

X thermal expansion.
g loss of mass of glaciers and ice caps.
G loss of mass of the Greenland ice sheet due to projected and recent
climate change.
A loss of mass of the Antarctic ice sheet due to projected and recent
climate change.
I loss of mass of the Greenland and Antarctic ice sheets
due to the ongoing adjustment to past climate change.
p runoff from thawing of permafrost.
s deposition of sediment on the ocean floor.

The components X, g, G and A are estimated for each of 35 SRES scenarios using
the projections of an upwelling-diffusion energy-balance (UD/EB) model calibrated
separately for each of seven AOGCMs (Appendix 9.1).

No uncertainty is included in this term, because the uncertainty is sufficiently
represented by the use of a range of AOGCMs. The term g from glaciers and ice
caps is estimated using the global average temperature change Tm(t)
projected by the UD/EB model. First, we obtain the loss of mass gu with respect
to the glacier steady state without taking contraction of glacier area into
account.

where g1990 is the sea-level rise from glaciers and ice caps
up to 1990 calculated from AOGCM results without contraction of glacier area,
T1990 is the AOGCM global average temperature change at 1990
with respect to the climate of the late 19th century, Tb
= 0.15 K the difference in the global average temperature between the late 19th
century and the glacier steady state (see 11.5.1.1)
and ðBg/ðTg is the sensivity of
global glacier mass balance for constant glacier area to global-average temperature
change, expressed as sea level equivalent (from Table
11.11). Second, we estimate the loss of mass g s with respect to the glacier
steady state taking into account contraction of glacier area. This is done by
using an empirical relationship between the loss of mass for changing and for
constant area. The relationship was obtained by a quadratic fit to the AOGCM
IS92a results of Section 11.5.1.1.

for gu and gs in metres. Third, we calculate the change
since 1990.

The uncertainty g(t)
on this term is calculated assuming an uncertainty of ±40% (standard
deviation) in the mass balance sensitivities, as discussed in Section
11.5.1.1.

The term G from the Greenland ice sheet is calculated according to

where dBG/dTg is the sensitivity of the Greenland mass
balance to global-average temperature change, expressed as sea level equivalent
(from Table 11.12). The uncertainty on this term
comprises two components, as discussed in Section 11.5.1.1.
The first uncertainty is a mass balance uncertainty

where mG
= 0.05 mm/yr/°C and TG/Tg
is the ratio of Greenland average temperature change to global average temperature
change (from Table 11.12). The first uncertainty
is the combination in quadrature of 0.03 mm/yr/°C from ablation parametrization,
0.03 mm/yr/°C from high-resolution patterns, and 0.02 mm/yr/°C from
precipitation changes, as discussed in section 11.5.1.1.
The second uncertainty is an ice-dynamic uncertainty.

The term A from the Antarctic ice sheet is calculated according to

where dBA/dTg is the sensitivity of the
Antarctic mass balance to global-average temperature change, expressed as sea
level equivalent (from Table 11.12). Ice-dynamical
uncertainty for the Antarctic is not included and is discussed in Section
11.5.4.3. There is no uncertainty for ablation. Precipitation change uncertainty
is calculated as discussed in Section 11.5.1.1 according
to

where mA
= 0.08 mm/yr/°C and TA/Tg
is the ratio of Antarctic average temperature change to global average temperature
change (from Table 11.12).

The uncertainties on the above terms are combined in quadrature:

The remaining terms are calculated assuming they contribute to sea-level rise
at a constant rate, independent of AOGCM and scenario, thus:

The rates each have a range of uncertainty. For dI/dt,
this is 0.0 to 0.5 mm/yr (Section 11.3.1, Table
11.9), for dp/dt 0 to 0.23 mm/yr (the
upper bound is more precisely 25 mm divided by 110 years, section
11.2.5), for ds/dt 0 to 0.05 mm/yr (Section
11.2.6, Table 11.9). The central rates are
0.25, 0.11 and 0.025 mm/yr for the three terms. We denote I calculated
at the minimum rate by Imin and at the maximum rate by Imax;
similarly for p and s. The minimum projected sea-level rise hmin(t)
for a given AOGCM and SRES scenario is given by

and the maximum is

In these formulae, hv
has been doubled to convert from an uncertainty to a range, following Box
11.1.